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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = (64 − x^2)^(1/4), y = 0, x = 6, x = 7; about the x-axis

  • Math -

    v = ∫[6,7] πr^2 dx
    where r = y = ∜(64-x^2)

    v = π∫[6,7] √(64-x^2) dx
    = π(1/2 √(64-x^2) + 32 arcsin(x/8)) [6,7]
    = π(√15/2 - √7 + 32(arcsin(7/8)-arcsin(3/4)))

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